Accumulative Temporal Decisions: A Discrete Field Theory on the Tesseract Graph with Emergent Lorentz Invariance and Ghost Elimination
Year: 2026
Type: preprint
Abstract: We propose a discrete field theory in which time is generated by an accumulative sequence of orthogonal decisions. The decision graph corresponds geometrically to a four-dimensional hypercube (tesseract): 16 vertices, 32 edges, and 8 cubic cells. On this graph we define a complex scalar field with a purely kinetic discrete action. The spectrum of the graph Laplacian yields a discrete mass spectrum m_k^2 = 4k (k=0,1,2,3,4), connected to the 16 one-dimensional representations of the tesseract automorphism group B_4. Crystallization is defined as an orthogonal projector onto the subspace of trajectories satisfying the orthogonality condition, eliminating 56 ghost trajectories and retaining 8 physical ones. In the continuum limit, three orthogonal spatial directions span a three-dimensional Euclidean space, the accumulative parameter yields the time dimension, and the metric emerges as ds^2 = \sum dx_i^2 - c^2 dt^2, with Lorentz invariance appearing as a low-energy effective symmetry. The model yields four falsifiable predictions: a discrete mass spectrum, density-of-states peaks, the absence of ghosts (m^2 \geq 0), and the monotonicity of the arrow of time. This framework is combinatorial and discrete-field-theoretic, not a complete quantum gravity theory; its value lies in providing a computable, falsifiable physical formalization of the intuition that time is an accumulative sequence of orthogonal decisions. Keywords: discrete spacetime; tesseract graph; lattice field theory; emergent Lorentz invariance; quantum gravity phenomenology; arrow of time; foundations of physics; mathematical physics
Author: HERRERA GONZÁLEZ, MICHEL ERNESTO
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224183167